Measuring novel configuration of points
You can define different measures in this way:

Maximum distance of the new point with all points of the configuration ($M$)
Minimum distance of the new point with all points of the configuration ($N$)
$\frac{M}{\text{Maximum distance between two points of the configuration(}D)}$: normalize (1) measure
$\frac{N}{D}$:normalize (2) measure

You can get more ideas from distance measures in hierarchical clustering methods. To select a proper one, you need to elaborate on the context of these points.